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{ SPLINE_BDRY.PDE

 

 This example shows the use of the SPLINE statement in constructing boundary curves.

 

 A circular arc is approximated by five spline segments.

 The end segments are made very short to establish the proper slope at the ends.

 

 The problem solves a heatflow equation on a quarter circle and compares the solution  

 with the analytic value.

 

}  

 

title 'Spline Boundary'  

 

Variables  

   u  

 

definitions  

   k = 1  

   u0 = 1-r^2  

   s = 4  

 

equations  

   U: div(k*grad(u)) + s  = 0  

 

boundaries  

  Region 1  

      start(0,0)  

      natural(u) = 0 line to (1,0)  

      value(u)=0  

      spline to(0.99985,0.01745) ! short initial interval to establish slope

              to (0.866,0.5)  

              to(0.5,0.866)  

              to (0.01745,0.99985)   ! short final interval to establish slope

              to (0,1)  

      natural(u)=0 line to close  

 

monitors  

  grid(x,y)  

  contour(u)  

  contour(u-u0)  

plots  

  grid(x,y)  

  contour(u)  

  contour(u-u0)  

end